Sequential Integrated Fault Tolerance Algorithm And Channel Coding Analysis

The Synthesis of linear shift register with error tolerance is an important problem in the analysis of stream cipher. In this paper, the authors construct a Homogenous Key Equation which is described by homogenous ideal of F[x,y], where F is a field. It is showed that the Homogenous Key Module Equation can be used to solve the synthesis problem of the linear shift register sequence. By means of a fast computation of Grobner basis of homogenous polynomial ideal with two variables, the authors find an efficient algorithm to solve the Homogenous Key Module Equation. We give a theorem to show the error tolerance of the algorithm in this paper. The simulation results show that the success rate of the algorithm has a linear relationship with the complexity of the sequence. For a sequence with length of1000and complexity of65, the success rate of the algorithm is up to86.6%at an error code rate of10-3.Based on this algorithm, we give a new algorithm to solve the Multi-Sequence Linear Shift-Register Synthesis problem. This algorithm can be used in the varying length case. The idea of the algorithm is very clear so that it can be understanded easily. It is an innovative algorithm. As the simulation results show, using the Grobner basis algorithm to resolve the multi-sequence synthesis has the same structure of the error tolerance.The research about the synthesis of linear shift register is complete while the research about the error tolerance of the algorithem is rare. This part of research can not only help on the stream cipher area but also be an important part of channel coding. In this paper, we also introduced some research work on the blind recognition of channel coding.Reed-Soloman (RS) code is an important code in channel coding with some excellent nature. We calculate the generator polynomial of the RS code using the Euclid algorithm. Based on this idea, we give a method to implement the blind recognition of RS code. This method has been used in an863national key project. We also used the parallel computing capability of GPU to decode the RS code. This method based on GPGPU can achieve several times speed up of the RS decoding.Gold code is one kind of scramblers. It is based on two LRS sequences. Because of its clear structure and diversity of the sequence, Gold code gets widely used, such as CDMA and radar system. In this paper, we introduced a method using Grobner basis algorithm to recognize the LRS generators of the two sequences and their initial states. It is a polynomial complexity algorithm with no restraint of the maximum degree of the polynomial, which is required in the traditional algorithms. In this paper, some theorems are also given to prove the feasibility of the algorithm.